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> half will by definition do "above average", and the other will do "below average" Is this really true? I think it's only true if you replace average with med

• dragonwriter 10y ago
  "Average" can refer to the median, or any of the various means. Its often informally used to mean the arithmetic mean (but also often the median), but it doesn't explicitly mean either of those.
• e12e 10y ago
  A very good point! I would say that it depends on what the distribution looks like, I wrote: > [I]f all of the "passive" half have a different random subset, then about half will by definition do "above average", and the other will do "below average". While in the "active group", less than half will do "above average" because they pay part of their gain to fund managers. So, if all the passive investors have pick a random "large enough" subset of stocks, one would expect the distribution to approach the normal distribution, with roughly half to either side of the arithmetic mean. Similarly, as you point out, on the "active" side, one might see more outliers - and perhaps the selection isn't really uniformly random. So, it would probably be a stretch to claim that half will be above average "by definition", even if one includes the expected distribution, while note perhaps entirely wrong.